Thermodynamics and Statistical Mechanics
I grew up with a physicist for a father, and to me it was natural to see physics as underlying every last thing that happened in the universe. Even as a very young boy, I knew from popular science books that chemical reactions were a consequence of the physics of interacting atoms, and when I became more sophisticated, I saw molecular biology as the result of the laws of physics acting on complex molecules. In short, I grew up seeing no room for “extra” forces in the world, over and above the four basic forces that physicists had identified (gravity, electromagnetism, and two types of nuclear force — strong and weak).
But how, as I grew older, did I reconcile that rock-solid belief with my additional convictions that evolution caused hearts to evolve, that religious dogmas have caused wars, that nostalgia inspired Chopin to write a certain étude, that intense professional jealousy has caused the writing of many a nasty book review, and so forth and so on? These easily graspable macroscopic causal forces seem radically different from the four ineffable forces of physics that I was sure caused every event in the universe.
The answer is simple: I conceived of these “macroscopic forces” as being merely ways of describing complex patterns engendered by basic physical forces, much as physicists came to realize that such macroscopic phenomena as friction, viscosity, translucency, pressure, and temperature could be understood as highly predictable regularities determined by the statistics of astronomical numbers of invisible microscopic constituents careening about in spacetime and colliding with each other, with everything dictated by only the four basic forces of physics.
I also realized that this kind of shift in levels of description yielded something very precious to living beings: comprehensibility. To describe a gas’s behavior by writing a gigantic piece of text having Avogadro’s number of equations in it (assuming such a herculean feat were possible) would not lead to anyone’s understanding of anything. But throwing away huge amounts of information and making a statistical summary could do a lot for comprehensibility. Just as I feel comfortable referring to “a pile of autumn leaves” without specifying the exact shape and orientation and color of each leaf, so I feel comfortable referring to a gas by specifying just its temperature, pressure, and volume, and nothing else.
All of this, to be sure, is very old hat to all physicists and to most philosophers as well, and can be summarized by the unoriginal maxim Thermodynamics is explained by statistical mechanics, but perhaps the idea becomes somewhat clearer when it is turned around, as follows: Statistical mechanics can be bypassed by talking at the level of thermodynamics.
Our existence as animals whose perception is limited to the world of everyday macroscopic objects forces us, quite obviously, to function without any reference to entities and processes at microscopic levels. No one really knew the slightest thing about atoms until only about a hundred years ago, and yet people got along perfectly well. Ferdinand Magellan circumnavigated the globe, William Shakespeare wrote some plays, J. S. Bach composed some cantatas, and Joan of Arc got herself burned at the stake, all for their own good (or bad) reasons, none of which, from their point of view, had the least thing to do with DNA, RNA, and proteins, or with carbon, oxygen, hydrogen, and nitrogen, or with photons, electrons, protons, and neutrons, let alone with quarks, gluons, W and Z bosons, gravitons, and Higgs particles.
Thinkodynamics and Statistical Mentalics
It thus comes as no news to anyone that different levels of description have different kinds of utility, depending on the purpose and the context, and I have accordingly summarized my view of this simple truth as it applies to the world of thinking and the brain: Thinkodynamics is explained by statistical mentalics, as well as its flipped-around version: Statistical mentalics can be bypassed by talking at the level of thinkodynamics.
What do I mean by these two terms, “thinkodynamics” and “statistical mentalics”? It is pretty straightforward. Thinkodynamics is analogous to thermodynamics; it involves large-scale structures and patterns in the brain, and makes no reference to microscopic events such as neural firings. Thinkodynamics is what psychologists study: how people make choices, commit errors, perceive patterns, experience novel remindings, and so on.
By contrast, by “mentalics” I mean the small-scale phenomena that neurologists traditionally study: how neurotransmitters cross synapses, how cells are wired together, how cell assemblies reverberate in synchrony, and so forth. And by “statistical mentalics”, I mean the averaged-out, collective behavior of these very small entities — in other words, the behavior of a huge swarm as a whole, as opposed to a tiny buzz inside it.
However, as neurologist Sperry made very clear in the passage cited above, there is not, in the brain, just one single natural upward jump, as there is in a gas, all the way from the basic constituents to the whole thing; rather, there are many way-stations in the upward passage from mentalics to thinkodynamics, and this means that it is particularly hard for us to see, or even to imagine, the ground-level, neural-level explanation for why a certain professor of cognitive science once chose to reshelve a certain book on the brain, or once refrained from swatting a certain fly, or once broke out in giggles during a solemn ceremony, or once exclaimed, lamenting the departure of a cherished co-worker, “She’ll be hard shoes to fill!”
The pressures of daily life require us, force us, to talk about events at the level on which we directly perceive them. Access at that level is what our sensory organs, our language, and our culture provide us with. From earliest childhood on, we are handed concepts such as “milk”, “finger”, “wall”, “mosquito”, “sting”, “itch”, “swat”, and so on, on a silver platter. We perceive the world in terms of such notions, not in terms of microscopic notions like “proboscis” and “hair follicle”, let alone “cytoplasm”, “ribosome”, “peptide bond”, or “carbon atom”. We can of course acquire such notions later, and some of us master them profoundly, but they can never replace the silver-platter ones we grew up with. In sum, then, we are victims of our macroscopicness, and cannot escape from the trap of using everyday words to describe the events that we witness, and perceive as real.
This is why it is much more natural for us to say that a war was triggered for religious or economic reasons than to try to imagine a war as a vast pattern of interacting elementary particles and to think of what triggered it in similar terms — even though physicists may insist that that is the only “true” level of explanation for it, in the sense that no information would be thrown away if we were to speak at that level. But having such phenomenal accuracy is, alas (or rather, “Thank God!”), not our fate.
We mortals are condemned not to speak at that level of no information loss. We necessarily simplify, and indeed, vastly so. But that sacrifice is also our glory. Drastic simplification is what allows us to reduce situations to their bare bones, to discover abstract essences, to put our fingers on what matters, to understand phenomena at amazingly high levels, to survive reliably in this world, and to formulate literature, art, music, and science.
CHAPTER 3
The Causal Potency of Patterns
The Prime Mover
AS THE rest of this book depends on having a clear sense for the interrelationships between different levels of description of entities that think, I would like to introduce here a few concrete metaphors that have helped me a great deal in developing my intuitions on this elusive subject.
My first example involves the familiar notion of a chain of falling dominos. However, I’ll j azz up the standard image a bit by stipulating that each domino is spring-loaded in a clever fashion (details do not concern us) so that whenever it gets knocked down by its neighbor, after a short “refractory” period it flips back up to its vertical state, all set to be knocked down once more. With such a system, we can implement a mechanical computer that works by sending signals down stretches of dominos that can bifurcate or join together; thus signals can propagate in loops, jointly trigger ot
her signals, and so forth. Relative timing, of course, will be of the essence, but once again, details do not concern us. The basic idea is just that we can imagine a network of precisely timed domino chains that amounts to a computer program for carrying out a particular computation, such as determining if a given input is a prime number or not. (John Searle, so fond of unusual substrates for computation, should like this “domino chainium” thought experiment!)
Let us thus imagine that we can give a specific numerical “input” to the chainium by taking any positive integer we are interested in — 641, say — and placing exactly that many dominos end to end in a “reserved” stretch of the network. Now, when we tip over the chainium’s first domino, a Rube Goldberg–type series of events will take place in which domino after domino will fall, including, shortly after the outset, all 641 of the dominos constituting our input stretch, and as a consequence various loops will be triggered, with some loop presumably testing the input number for divisibility by 2, another for divisibility by 3, and so forth. If ever a divisor is found, then a signal will be sent down one particular stretch — let’s call it the “divisor stretch” — and when we see that stretch falling, we will know that the input number has some divisor and thus is not prime. By contrast, if the input has no divisor, then the divisor stretch will never be triggered and we will know the input is prime.
Suppose an observer is standing by when the domino chainium is given 641 as input. The observer, who has not been told what the chainium was made for, watches keenly for while, then points at one of the dominos in the divisor stretch and asks with curiosity, “How come that domino there is never falling?”
Let me contrast two very different types of answer that someone might give. The first type of answer — myopic to the point of silliness — would be, “Because its predecessor never falls, you dummy!” To be sure, this is correct as far as it goes, but it doesn’t go very far. It just pushes the buck to a different domino, and thus begs the question.
The second type of answer would be, “Because 641 is prime.” Now this answer, while just as correct (indeed, in some sense it is far more on the mark), has the curious property of not talking about anything physical at all. Not only has the focus moved upwards to collective properties of the chainium, but those properties somehow transcend the physical and have to do with pure abstractions, such as primality.
The second answer bypasses all the physics of gravity and domino chains and makes reference only to concepts that belong to a completely different domain of discourse. The domain of prime numbers is as remote from the physics of toppling dominos as is the physics of quarks and gluons from the Cold War’s “domino theory” of how communism would inevitably topple country after neighboring country in Southeast Asia. In both cases, the two domains of discourse are many levels apart, and one is purely local and physical, while the other is global and organizational.
Before passing on to other metaphors, I’d just like to point out that although here, 641’s primality was used as an explanation for why a certain domino did not fall, it could equally well serve as the explanation for why a different domino did fall. In particular, in the domino chainium, there could be a stretch called the “prime stretch” whose dominos all topple when the set of potential divisors has been exhausted, which means that the input has been determined to be prime.
The point of this example is that 641’s primality is the best explanation, perhaps even the only explanation, for why certain dominos did fall and certain other ones did not fall. In a word, 641 is the prime mover. So I ask: Who shoves whom around inside the domino chainium?
The Causal Potency of Collective Phenomena
My next metaphor was dreamt up on an afternoon not long ago when I was caught in a horrendous traffic jam on some freeway out in the countryside, with several lanes of nearly touching cars all sitting stock still. For some reason I was reminded of big-city traffic jams where you often hear people honking angrily at each other, and I imagined myself suddenly starting to honk my horn over and over again at the car in front of me, as if to say, “Get out of my way, lunkhead!”
The thought of myself (or anyone) taking such an outrageously childish action made me smile, but when I considered it a bit longer, I saw that there might be a slim rationale for honking that way. After all, if the next car were magically to poof right out of existence, I could fill the gap and thus make one car-length’s worth of progress. Now a car poofing out of existence is not too terribly likely, and one car-length is not much progress, but somehow, through this image, the idea of honking became just barely comprehensible to me. And then I remembered my domino chainium and the silly superlocal answer, “That domino didn’t fall because its neighbor didn’t fall, you dummy!” This myopic answer and my fleeting thought of honking at the car just ahead of me seemed to be cut from the same cloth.
As I continued to sit in this traffic jam, twiddling my thumbs instead of honking, I let these thoughts continue, in their bully-like fashion, to push my helpless neurons around. I imagined a counterfactual situation in which the highway was shrouded in the densest pea-soup fog imaginable, so that I could barely make out the rear of the car ahead of me. In such a case, honking my horn wouldn’t be quite so blockheaded. For all I know, that car alone might well be the entire cause of my being stuck, and if only it would just get out of the way, I could go sailing down the highway!
If you’re totally fog-bound like that, or if you’re incredibly myopic, then you might think to yourself, “It’s all my neighbor’s fault!”, and there’s at least a small chance that you’re right. But if you have a larger field of view and can see hordes of immobilized cars on all sides, then honking at your immediate predecessor is an absurdity, for it’s obvious that the problem is not local. The root problem lies at some level of discourse other than that of cars. Though you may not know its nature, some higher-level, more abstract reason must lie behind this traffic jam.
Perhaps a very critical baseball game just finished three miles up the road. Perhaps it’s 7:30 on a weekday morning and you’re heading towards Silicon Valley. Perhaps there’s a huge blizzard ten miles ahead. Or it may be something else, but it’s surely some social or natural event of the type that induces large numbers of people all to do the same thing as one another. No amount of expertise in car mechanics will help you to grasp the essence of such a situation; what is needed is knowledge of the abstract forces that can act on freeways and traffic. Cars are just pawns in the bigger game and, aside from the fact that they can’t pass through each other and emerge intact post-crossing (as do ripples and other waves), their physical nature plays no significant role in traffic jams. We are in a situation analogous to that in which the global, abstract, math-level answer “641 is prime” is far superior to a local, physical, domino-level answer.
Neurons and Dominos
The foregoing down-to-earth images provide us with helpful metaphors for talking about the many levels of causality inside a human brain. Suppose it were possible to monitor any selected neuron in my brain. In that case, someone might ask, as I listened to some piece of music, “How come neuron #45826493842 never seems to fire?” A local, myopic answer might be, “Because the neurons that feed into it never fire jointly”, and this answer would be just as correct but also just as useless and uninformative as the myopic answers in the other situations. On the other hand, the global, organizational answer “Because Doug Hofstadter doesn’t care for the style of Fats Domino” would be much more on target.
Of course we should not fall into the trap of thinking that neuron #45826493842 is the sole neuron designated to fire whenever I resonate to some piece of music I’m listening to. It’s just one of many neurons that participate in the high-level process, like voters in a national election. Just as no special voter makes the decision, so no special neuron is privileged. As long as we avoid simplistic notions such as a privileged “grand-music neuron”, we can use the domino-chainium metaphor to think about brains, and especially
to remind ourselves of how, for a given phenomenon in a brain, there can be vastly different explanations belonging to vastly different domains of discourse at vastly different levels of abstraction.
Patterns as Causes
I hope that in light of these images, Roger Sperry’s comments about “the population of causal forces” and “overall organizational forces and dynamic properties” in a complex system like the brain or the chainium have become clearer. For instance, let us try to answer the question, “Can the primality of 641 really play a causal role in a physical system?” Although 641’s primality is obviously not a physical force, the answer nonetheless has to be, “Yes, it does play a causal role, because the most efficient and most insight-affording explanation of the chainium’s behavior depends crucially on that notion.” Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.
I have to emphasize that there’s no “extra” physical (or extra-physical) force here; the local, myopic laws of physics take care of everything on their own, but the global arrangement of the dominos is what determines what happens, and if you notice (and understand) that arrangement, then an insight-giving shortcut to the answer of the non-falling domino in the divisor stretch (as well as the falling domino in the prime stretch) is served to you on a silver platter. On the other hand, if you don’t pay attention to that arrangement, then you are doomed to taking the long way around, to understanding things only locally and without insight. In short, considering 641’s primality as a physical cause in our domino chainium is analogous to considering a gas’s temperature as a physical cause (e.g., of the amount of pressure it exerts against the walls of its container).
I Am a Strange Loop Page 7
